EXCHANGE 


"University  of  Cbtcaoo 


OX   THE    MOTION  OF   A   SPHERE    OF  Oil 

THROUGH  CARBON  DIOXIDE  AND  AN 

EXACT  DETERMINATION  OF  THE 

COEFFICIENT  OF  VISCOSITY 

OF  THAT  GAS  BY  THE 

OIL  DORP  METHOD 


LEO  JOSEPH   LASSALLK 


A    DISSERTATION 

SUBMITTED  TO  THE  FACULTY  OF  THE  OGDEN  GRADUATE  SCHOOL  OF  SCIENCE 

IN  CANDIDACY  FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY, 

DEPARTMENT  OF   PHYSICS 


CHICAC.O 
1917 


tlbe  Tllnlversitg  of  Cbtcago 


ON  THE    MOTION  OF  A  SPHERE   OF  OIL 

THROUGH  CARBON  DIOXIDE  AND  AN 

EXACT  DETERMINATION  OF  THE     • 

COEFFICIENT  OF  VISCOSITY 

OF  THAT  GAS  BY  THE 

OIL  DORP  METHOD 


BY 

LEO  JOSEPH  LASSALLE 


A    DISSERTATION 

SUBMITTED  TO  THE  FACULTY  OF  THE  OGDEN  GRADUATE  SCHOOL  OF  SCIENCE 

IN  CANDIDACY  FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY, 

DEPARTMENT  OF  PHYSICS 


CHICAGO 
1917 


of, 


ON  THE  MOTION  OF  A  SPHERE  OF  OIL  THROUGH  CAR- 
BON DIOXIDE  AND  A  DETERMINATION  OF  THE 
COEFFICIENT  OF  VISCOSITY  OF  THAT 
GAS  BY  THE  OIL  DROP  METHOD. 


458684 


[Reprinted  Jrom  the  PHYSICAL  REVIEW,  N.S..  Vol.  XVII,  No.  3,  March,  1921.] 


ON  THE  MOTION  OF  A  SPHERE  OF  OIL  THROUGH   CAR- 
BON  DIOXIDE  AND  A   DETERMINATION   OF  THE 
COEFFICIENT  OF  VISCOSITY   OF  THAT 
GAS   BY  THE  OIL   DROP   METHOD. 

BY  LEO  JOSEPH  LASSALLE. 

SYNOPSIS. 

i  I.  Coefficient  of  Viscosity  of  CO z  by  the  Oil-drop  Method. — The  value  of  e  being 
known,  through  work  in  air,  to  an  accuracy  of  about  .1  per  cent.,  the  oil-drop  method 
as  developed  by  Millikan  has  been  used  in  COz  for  the  determination  of  the  coefficient 
of  vicsosity  of  that  gas  with  the  result  at  23°  C.  77  =  1.490  X  io~4. 

II.  Coefficient  of  Slip  between  CO?,  and  Oil. — The  value  of  the  constant  A  in 
Millikan's  equation  e\  =  e(i  +  AZ/o)3/2  is  found  in  COa  to  be  0.8249  as  against 
Millikan's  value  in  air  0.864. 

III.  Variability  of  the  Constant  A  for  Values  of  I/a  Greater  than  .5. — Precisely  as 
in  Millikan's  work  in  air,  A  was  found  to  be  constant  only  up  to  I/a  =  .5,  beyond 
which  it  kept  increasing  as  far  as  it  was  followed,  viz.,  up  to  I/a  =  12. 

INTRODUCTION. 

THE  behavior  of  oil  drops  falling  in  air  has  been  reported  upon  by  R. 
A.  Millikan.1  Every  precaution  possible  was  taken  to  assure  the 
highest  degree  of  accuracy.  The  value  of  e  obtained  was  shown  to  be 
accurate  to  within  0.2  of  one  per  cent.  The  law  of  fall  for  oil  drops  in 
hydrogen  was  investigated  by  R.  A.  Millikan,  W.  H.  Barber,  and  Y. 
Ishida.2  The  same  precautions  as  those  taken  for  air  were  observed. 

The  work  here  described  was  undertaken  at  the  suggestion  of  Dr. 
Millikan  in  order  to  find  the  correction  factor  to  Stoke 's  law  for  carbon 
dioxide,  and  the  coefficient  of  viscosity  of  that  gas  by  a  new  method. 

The  value  of  e?lz  is  directly  proportional  to  the  coefficient  of  viscosity, 
77,  of  the  gas  used.  As  is  shown  later,  this  relationship  furnishes  an 
elegant  method  of  determining  77  for  any  gas,  and  is  used  in  this  paper 
to  obtain  the  viscosity  coefficient  for  CO2  at  23°  C. 

The  apparatus  used  was  the  same  one  used  by  R.  A.  Millikan.3  The 
same  precautions  were  taken  to  give  as  high  a  degree  of  accuracy  as 

1  "On  the  Elementary  Electrical  Charge  and  The  Avagadro  Constant,"  PHYSICAL  REVIEW, 
N.S.,  Vol.  II.,  No.  2,  Aug.,  1913,  p.  109. 

2  "The  Law  of  Fall  of  a  Droplet  Through  Hydrogen,"  PHYSICAL  REVIEW,   Series  2,  5, 
-  P-  334- 

»  PHYS.  REV.,  N.S.,  Vol.  II.,  No.  2,  Aug.,  1913,  p.  109. 


MOTION   OF  A    SPHERE   OF   OIL.  355 

possible.  All  of  the  time  observations  were  taken  with  a  Gaertner 
recording  chronograph.  This  instrument  records  time  to  one  one- 
hundredth  of  a  second.  It  was  adjusted  so  as  never  to  be  in  error  by 
more  than  two  hundred  ths  of  a  second  per  minute. 

The  following  method  described  by  Langmuir  was  used  in  generating 
the  CO2.  Using  a  Kipp  generator,  CaCO3  +  2HNO3  =  CO2  +  Ca(NO3)2 
+  H2O  +  HNO3  vapor  +  H2O  vapor.  The  gas  is  bubbled  through 
NaHCO3,  which  takes  up  acid  vapors  but  no  CO2;  then  it  passes  through 
P2O5  tubes  which  take  up  all  H2O  vapor. 

The  HNO3  was  a  50  per  cent,  pure  H2O  solution  through  which  com- 
mercial CO2  had  been  bubbled  for  5  hours  before  being  put  into  the  Kipp 
generator.  The  CaCO3  (marble)  was  broken  and  boiled  4  hours  in  a 
very  dilute  solution  of  HNO3.  The  vessels  into  which  the  gas  was  intro- 
duced were  evacuated  to  a  pressure  below  0.5  mm.  before  they  were  filled. 
They  were  then  pumped  down  again  to  the  same  low  pressure  and 
refilled  with  CO2.  This  process  was  repeated  three  times  before  any 
observations  were  taken,  thus  assuring  that  not  more  than  one  part  of 
air  in  (i.soo)3  parts  of  CO2  remained  in  the  vessels. 

For  a  complete  discussion  of  the  apparatus  used  and  the  precautions 
taken  to  assure  accuracy  in  the  determinations  of  the  constants  that 
enter  into  the  following  results  see  paper  by  R.  A.  Millikan.1 

PART  I. 

Determination  of  Coefficient  of  Viscosity  of  COz- 

Oil  droplets  were  obtained  for  observation  by  aspirating  oil  with  CO2 
gas  under  pressure.  They  were  held  for  a  sufficient  length  of  time  to 
observe  the  time  of  fall  under  gravity  (/„)  on  an  average  of  eighteen  times. 
The  average  number  of  changes  of  charge  obtained  for  each  drop  was 
seven  for  the  first  thirty-six  drops,  which  are  the  ones  used  in  the  deter- 
mination of  the  coefficient  of  viscosity  and  the  correction  factors  "b" 
and  "A." 

The  results  of  the  observations  were  such  as  to  leave  no  uncertainty 
as  to  the  greatest  common  divisor  of  [(i/tg)  -f  (i  ///)],  which  will  be 
represented  hereafter  by  [(!//„)  +  (iA/)]o,  and  which  is  the  variable 
factor  upon  which  the  value  of  (ei2/3/i?)  and  (a)  are  dependent. 

It  is  significant  that  these  thirty-six  drops  represent  every  drop 
observed  where  P.D.  was  constant  to  as  much  as  0.4  of  one  per  cent,  and 
where  as  many  as  three  changes  of  charge  were  obtained.  In  the  equation 

(».  +  ».)•(».)"' 


1  R.  A.  Millikan,  PHYS.  REV.,  N.S.,  Vol.  II.,  No.  2,  Aug.,  1913,  pp.  109-143;    also  Phil. 
Mag.,  XXXIV.,  p.  13,  1917- 


356  LEO  JOSEPH  LASSALLE. 

771  is  the  coefficient  of  viscosity  of  CO2  at  23°  C.,  g  the  acceleration  due 
to  gravity,  <r  the  density  of  the  oil,  p  the  density  of  the  CO2,  v\  the  speed 
of  descent  of  the  drop  under  gravity  and  vz  the  speed  of  ascent  under 
the  action  of  the  electrical  field  of  strength  F. 

If  we  now  allow  e\  to  be  the  greatest  common  divisor  of  all  the  various 
values  of  en  found  on  a  drop  during  the  observations  upon  it,  and  if  we  let 

_D_ 

_D_ 

Vz  ~  tf  ' 
and 


d    ' 

where  D  is  the  distance  the  drop  falls  in  time  ta  and  the  distance  it  rises 
in  time  tf,  and  d  is  the  distance  between  the  two  parallel,  horizontal 
condenser  plates,  between  which  a  difference  of  potential  in  volts,  repre- 
sented by  P.D.,  is  maintained  by  means  of  storage  cells  which  do  not 
change  more  than  four  parts  in  a  thousand  during  a  series  of  observations 
on  a  given  drop,  then  equation  (i)  may  be  written  in  the  form 


9 


where  [(i/ta)  +  (i///)]0  is  the  greatest  common  divisor  of  [(i/ta)  + 
for  the  given  drop. 

Equation  (2)  may  be  written 


This  gives  a  simple  method  of  calculating 

a,  the  radius  of  the  falling  drop,  is  calculated  by  means  of  the  expression 


77!  (P.D.)2/3 

where 

,1/3' 

C  =  I  -1 


(  N 

'  '  f 

which  may  be  written, 


The  pressure  of  the  gas  p  is  observed  directly. 


VOL.  XVII. 
No.  3. 


MOTION   OF  A    SPHERE   OF   OIL. 


357 


Table  I.  gives  the  values  of  the  factors  which  enter  into  the  deter- 
mination of  ei2/3/?7i  and  a,  as  well  as  into  the  values  of  e\zl3,  e\,  and  e213* 
The  last  three  values  can  only  be  obtained  after  T;I  and  b  have  been 
calculated. 

For  the  present  let  us  assume  that  the  table  does  not  contain  £i2/3, 
e\,  nor  e213,  and  plot  ei2/3/rji  against  i/pa.  Curve  I  shows  this  relationship. 


340       600 


Fig.  1. 

It  is  a  straight  line  which  crosses  the  ei2/3/*?i  axis  at  41.00  X  io~4. 
If  we  write 


2/3    _ 


then 


= 

pa 


It  is  evident  that,  for  i/pa  =  o, 

.,2/3 


»7 1 


We  are  justified  in  saying  that  the  value  of  the  elementary  electrical 
charge  on  an  oil  drop  is  independent  of  whether  it  be  in  CC>2  or  in  any 
other  gas,  say  air.  Since  the  value  of  e213  in  air  is  known  to  be  61.085 
X  io~8  E.  S.  units,  with  a  probable  error  of  less  than  o.i  of  one  per  cent.,1 
then  at  i/pa  =  o,  e^3  =  e2'3  =  61.085  X  io~8; 

.'.  —  =  41.00  X  io~4 

1  This  is  the  value  obtained  by  reducing  the  number  given  by  R.  A.  Millikan  in  Phil.  Mag., 
XXXIV.,  p.  13,  by  .07  per  cent,  to  allow  for  the  change  in  the  value  of  the  coefficient  viscosity 
of  air  from  .0001824  to  .00018227. 


LEO   JOSEPH   LASSALLE. 

gves 

61.085  X  io-8 

ill  =  -  —7  =  1.490  X  io~4, 

41.00  X  io~4 

which,  because  all  the  calculations  were  reduced  to  23°  C.,  gives  the 
value  of  the  coefficient  of  viscosity  at  23°  C. 

Wherever  the  temperature  differed  from  23°  C.  during  an  observation 
the  correction  factor  to  be  applied  to  the  value  of  171  was  introduced  into 
the  calculation  of  (0i2/3/T7i).  Sutherland's  equation  was  used  and  the 
variation  of  log  771  with  temperature  was  obtained  by  plotting  log  171 
against  temperature.  With  the  exception  of  drops  5  and  15,  which 
differ  by  about  i°  C.,  the  variation  from  23°  C.  was  always  less  than 
0.5°  C. 

By  the  oil  drop  method,  then,  the  value  of  the  coefficient  of  viscosity 
of  CO2  at  23°  C.  is  found  to  be 

l?C0jat23-(7  =    1-490   X    I0~4. 

The  accuracy  of  this  result  is  dependent  upon  the  accuracy  with 
which  the  value  of  e2/3  is  known  and  the  accuracy  with  which  the  inter- 
cept on  the  ei2/3/T7i  axis  for  CO2  is  known. 

e2/3  is  known  with  an  accuracy  of  about  o.i  of  one  per  cent.  The  ei2/3/7ji 
intercept  is  known  with  a  probable  error  of  about  0.5  of  one  per  cent. 
Therefore,  the  value  of  771  given  by  these  observations  should  be  accurate 
to  about  0.5  of  one  per  cent. 

Therefore 

*7co2at23'C  =  (1490  ±  0.0080)  X  io~4. 

Breitenbach1  obtained 


at  15o(7  =1457    X    I0~4. 

Applying  the  Sutherland  equation  to  his  value  there  results 

*?C02at23oC  =    1494   X    IO-4. 

If  we  assume  that  this  investigator's  value  is  too  high  for  CO2  in  the 
same  ratio  that  his  value  for  air  is  too  high,  we  get 

1786 
i?co2at23.c  =  (1494  X  iQ"4)  =  J474  X  io-4, 


a  value  I  per  cent,  lower  than  the  one  obtained  in  this  paper. 

Ernst  Thomson,2  using  a  vibrating  disc,  obtains  a  value  of  ij  for  CO2 
which  is  0.0000004  higher  than  Breitenbach's.  However,  the  main 
object  of  his  investigation  was  to  find  the  relationship  between  the  77  for 

1  Breitenbach,  Ann.  d.  Phys.,  5,  1901. 

*"Ueber  die  innere  Aeibung  von  Gasgemischen,"  Inaugural  Dissertation,  der  Konigl. 
Christian-Albrechts  Univ.  zu  Kiel. 


MOTION  OF   A    SPHERE   OF   OIL.  359 

two  gases  and  the  77  for  various  mixtures  of  these  two  gases.  He  does 
not  claim  any  high  degree  of  accuracy  for  his  value  of  the  coefficient  of 
viscosity  of  CO2. 

P.  Phillips1  gives  a  value  of  77  which  reduced  to  23°  C.  by  Sutherland's 
equation,  becomes 

*7CO,at23°C  =    1-494   X    I0~4. 

He  used  the  A.  O.  Rankin  device,2  which  is  a  capillary  tube  method. 
The  object  of  his  investigation  was  to  determine  the  variation  of  77  with 
pressure,  going  to  pressures  of  eighty  atmospheres.  No  high  degree  of 
accuracy  is  claimed  for  the  determination  of  the  77  at  atmospheric  pres- 
sure. The  important  point  sought  after  was  to  obtain  relative  values 
as  pressure  varied. 

If,  however,  we  take  the  mean  of  the  values  obtained  by  Breitenbach, 
Thomsen  and  Phillips,  a  value  of  77C02at23<>c  =  1-489  X  io~4  is  obtained. 
This  value  is  different  by  less  than  o.i  of  one  per  cent,  from  the  one  here 
obtained. 

PART  II. 

The  A  and  b  Correction  Terms  in  CO 2. 

Table  I.  gives  the  values  of  eiz'3/r]i  corresponding  to  the  various  values 
of  I / pa.  ei213  is  obtained  by  multiplying  ei2l3/iji  by  the  value  of  771  as 
found  in  part  I. 

Fig.  2  gives  the  result  of  plotting  e\-lz  against  i/pa. 

If,  now,  we  write 

/  T         \ 

(7) 

and  let  y  =  e^l3\  y0  =  e213,  and  x  =  (i/pa),  we  have  y  =  y0  +  byox.  By 
differentiation,  then,  the  above  becomes 

/  dy         \       Slope  of  (y,  x)  curve 

b  =  (  ~, —  ~j~  y  ]  ==  ~~      — . —  ~~  .  (8) 

\  dx         )  ^-intercept 

This  gives  a  simple  method  of  determining  the  correction  factor  &.3 
The  last  column  in  Table  I.  gives  the  values  of  e213  calculated  by  sub- 
stituting in  (7)  and  solving.  The  values  of  e  follow  directly  from  those 
of  e213.  It  will  be  noticed  that  no  value  of  e213  varies  from  61.085  by  as 
much  as  0.5  of  one  per  cent. 

The  value  of  b,  obtained  by  substituting  in  (8)  is 

_  Slope  of  y,  x  curve  _  (75-37  —  61.085) 
y-intercept  600  X  61.085 

1  P.  Phillips,  Roy.  Soc.  Proc.,  Ser.  A,  87.  pp.  48-61. 

s  Roy.  Soc.  Proc.,  1910,  A,  Vol.  83,  p.  265. 

'  R.  A.  Millikan,  PHYS.  REV.,  II.,  p.  118,  1913,  and  XXXII.,  p.  381,  1911. 


360 


LEO   JOSEPH   LASSALLE. 


(•SECOND 
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VOL.  XVII.1 
No.  3.          J 


MOTION   OF   A    SPHERE   OF   OIL. 


x  ,_;,_;  o  *-<  •«-<  *-<  o' 

M 

X 

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c 

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c 

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t 


LEO   JOSEPH   LASSALLE. 


[SECOND 

[SERIES. 


or 

b  =  0.0003898 
(see  Fig.  2). 

It  should  be  noticed  that  the  value  of  b  is  independent  of  any  theory 
and  is  determined  by  the  use  of  values  which  are  directly  measurable. 
If,  however,  it  is  desired  to  write  (7)  in  the  form 


,2/3    _ 


(9) 


then  A  can  be  calculated  in  the  same  way  that  b  was,  provided  the  values 
of  I/a  are  known. 

Using  77  =  o.35O2ww/C,  where  the  Boltzmann  value  of  K  is  used  so 


76 

TS 

74 

73 

7* 

fl 

70 

69 

6! 


66 


62] 


rtrf 


^ 


0      50    60    90 


300       360      420       480 


509 


Fig.  2. 

as  to  give  an  A  that  can  be  compared  with  that  for  air  obtained  by  R.  A. 
Millikan  in  the  paper  previously  referred  to,  the  values  of  I  [a  can  be 
calculated. 

From  equations  (7)  and  (9)  it  is  evident  that 


'--••=• 

a         pa 


(10) 


At  a  constant  temperature  i/pl  is  a  constant.  Therefore,  A  =  bB, 
which  means  that  the  (ei273,  ijpa)  curve  becomes  the  (ei2/3,  //a)  curve 
simply  by  changing  the  scale  of  the  abscissae. 

By  calculating  for  a  given  drop  and  substituting  in  equation  (10)  the 
value  of  A/b  =  B  is  obtained.  This  is  checked  by  making  the  calcu- 


VOL.  XVII 
No.  3. 


MOTION   OF  A    SPHERE   OF   OIL. 


363 


ation  for  several  drops.  In  this  way  B  was  found  to  be  equal  to  2116. 
This  gives  for  CO 

A  =  0.8249. 

The  value  obtained  by  R.  A.  Millikan  in  his  work  in  air  was  A  =  .864. 
The  difference  would  seem  to  be  slightly  more  than  the  experimental 
error  involved  in  the  determination  of  the  slope  of  the  line  from  which  A 
is  obtained.  This  error  should  scarcely  exceed  two  or  three  per  cent. 
There  is  then  here  a  somewhat  uncertain  indication  that  the  coefficient 
of  slip  between  CO2  and  oil  is  a  trifle  less  than  that  between  air  and  oil. 

TABLE  II. 


No. 

Temp. 

P.  D. 

Volts. 

(Sec.) 

X(§eV)- 

n 

aXlO5 
Cms. 

/  Cms. 
Hg. 

i 

a  ' 

-*•"• 

35 

22.70 

3245.0 

53.833  0.014186     3-9 

10.63 

16.70 

631.6 

0.2985     76.19 

36    23.04 

2604.8 

38.036  0.00971       3-13 

12.58 

12.02 

661.3 

0.3125 

77.01 

37    23.15 

2583.0 

22.63 

0.00771  ;     8-19 

16.11 

8.160 

760.83 

0.3595 

79.33 

38    23.15 

2589.5 

27.67 

0.00920       5-13 

14.22 

7.638 

921.09 

0.4352 

82.94 

39    22.90 

1288.5 

9.32 

0.00274     67-168 

24.24 

4.210 

980.14 

0.4632 

84.63 

40 

22.87 

1288.4 

14.83 

0.003817    18-66 

18.59 

4.588 

1172.5 

0.5540 

90.38 

41 

23.38 

1938.6 

24.02 

0.00735        7-13 

14.57 

5.566 

1233.3 

0.5828 

91.05 

42 

22.85 

1286.5 

20.81 

0.00460        8-56 

15.60 

5.279 

1214.6 

0.5739 

91.50 

43 

22.87 

1286.0 

26.67 

0.00560  |     7-87 

13.45 

5.365 

1386.1 

0.6550 

96.06 

44 

22.90 

1288.2 

20.36 

0.00514 

10-44 

15.15 

4.410 

1497.1 

0.7074 

99.18 

45 

23.35 

1933.3 

38.55 

0.01073 

3-12 

10.97 

5.910 

1542.7 

0.7290 

100.05 

46 

22.86 

1288.8 

19.20 

0.00522 

11-35 

15.37 

4.110 

1583.1 

0.7480 

102.14 

47 

22.80 

650.3 

7.01 

0.00169 

86-137 

24.94 

2.450 

1636.3 

0.7732 

106.2 

48 

22.85 

648.5 

16.91 

0.00298 

26-99 

15.37 

3.356 

1938.5 

0.9160 

115.9 

49 

22.74 

1289.5 

27.39 

0.00772 

5-33 

11.99 

3.860 

2161.6 

1.021 

117.8 

50 

22.79 

651.4 

10.19 

0.00254 

29-153 

19.22 

2.290 

2271.5 

,1.073 

123.0 

51 

22.90 

653.5 

9.58 

0.00267 

38-129 

19.32 

2.055 

2518.7 

1.190 

129.5 

52 

23.20 

92.70 

9.90 

0.000391 

240-376 

18.91 

1.970 

2684.7 

1.269 

131.0 

53 

22.83 

649.5 

23.23 

0.00530 

12-60 

11.42 

2.638 

3319.6 

1.569 

152.9 

54 

22.95 

656.7 

16.06 

0.00550 

12-44 

12.80 

1.990 

3925.1 

1.855 

176.0 

55 

22.79 

651.1 

42.68 

0.01510 

2-6 

6.58 

2.390 

6356.7 

3.004 

250.4 

56 

23.55 

649.8 

9.96 

0.00809 

12-31 

13.15 

1.060 

7171.5 

3.389 

269.3 

57 

22.08 

156.0 

31.26 

0.00364 

26-77 

7.29 

1.840 

7457.8 

3.524 

278.4 

58 

23.14 

155.72 

13.45 

0.00275 

37-159 

10.59 

1.100 

8582.6 

4.056 

307.2 

59 

22.83 

192.50 

7.18 

0.00117    122-225 

14.60 

0.798 

8584.2 

4.056 

302.7 

60 

22.90 

155.21 

6.87 

0.00241  j  64-122 

13.84 

0.719 

10051. 

4.750 

352.2 

61 

24.46 

157.00 

28.32 

0.00507  1     3-85 

6.76 

1.450 

10205. 

4.822 

359.9 

62 

23.22 

156.8 

13.23 

0.00469      17-27 

8.94 

0.736 

12076. 

5.706 

438.8 

63 

22.82 

652.2 

82.18 

0.05502        1-2 

3.44 

2.211 

13147. 

6.212 

476.1 

64 

22.86 

156.72 

13.03 

0.00571      14-18 

8.41 

0.841 

14142. 

6.683 

502.7 

65 

22.80 

158.22 

36.08 

0.01945       3-6 

3.99 

1.112 

22524. 

10.64 

805.2 

66 

23.02 

92.56 

9.87 

0.00708      14-27 

7.21 

0.540 

25702. 

12.14 

904.4 

67 

22.93 

89.97 

23.59 

0.01103 

2-8 

4.60 

0.824 

26552. 

12.55 

926.4 

LEO   JOSEPH   LASSALLE. 


PART  III. 


[SECOND 

[SERIES. 


Limits  to  the  Validity  of  Millikan's  Equation  in  CO  2. 

Observations  were  taken  on  drops  at  as  large  values  of  I/a  as  practicable 
with  the  method  of  obtaining  drops  that  was  used  throughout  these 
observations.  It  was  found  very  difficult  to  get  drops  at  pressure  below 
one  cm.  of  Hg.  A  more  direct  method  of  blowing  the  drops  and  one 
which  will  introduce  less  gas  into  the  system  is  desirable  in  order  to  go 
to  low  pressures. 

At  low  pressures  it  is  not  possible  to  have  such  high  potential  differ- 
ences; also  it  is  not  possible  to  observe  on  drops  of  the  same  size  as 
those  used  at  pressures  above,  say  2  cm.  These  two  factors  tend  to 
counterbalance  each  other  as  far  as  the  difficulty  of  observing  on  drops 
with  a  small  number  of  charges  is  concerned.  If  the  number  is  not 
small  the  greatest  common  divisor  of  the  series  of  speeds  begins  to  be 
uncertain.  However,  no  drop  was  used  in  these  calculations  where 
there  was  doubt  as  to  this  greatest  common  divisor. 

Table  II.  gives  the  values  of  the  various  factors  entering  into  the 


goo         /oao       /zco       MOD       1600       /goo       -?ooo      ,2400      Z400       £600 


Fig.  3. 

determinations  of  e^13,  i/pa  and  I/a  for  drops  where  the  values  of  i/pa 
are  greater  than  600. 

Fig-  3  gives  the  relationship  between  e^13  and  if  pa,  which  is  also  that 
between  ex2/3  and  I/a.  It  gives  this  relationship  from  i/pa  =  600  to 
i/pa  =  2,500.  It  will  be  seen  that  from  600  to  about  1,100  the  slope  is 
the  same  as  that  for  i/pa  =  o  to  i/pa  =  600.  But  at  about  the  value 
of  1,100  the  slope  clearly  begins  to  change.  This  behavior  is  quite  like 
that  found  by  R.  A.  Millikan  in  his  work  with  air.  He  found  (Pnvs. 


VOL.  XVII. 
No.  3. 


MOTION  OF   A    SPHERE   OF   OIL. 


365 


REV.,  II.,  p.  138)  that  the  linear  relation  between  eiw  and  i/pa  began 
to  break  down  at  about  i/pa  =  650,  which  corresponds  to  a  value  of  I/a 
of  about  .5.  Here  the  break  comes  at  about  i/pa  =  1,100  which  will 
be  seen  from  Table  II.  to  also  correspond  to  a  value  of  I /a  =  .5. 


J9foo      S3SOO 


Fig.  4. 

Fig.  4  shows  the  graph  of  the  relations  contained  in  Table  II.  in  the 
range  I/pa  =  2,500  up  to  if  pa  =  26,500,  i.e.,  in  the  range  I/a  =  I  to 

I/a  =  12. 

SUMMARY. 

I.  Using  the  oil-drop  method,  the  coefficient  of  viscosity,  ij,  of  CO2  at 
23°  C.  was  found  to  be  1.490  X  io~4. 

II.  The  correction  factors  b  and  A  as  given  in  the  equations 


2/3    _ 


and 


were  determined  for  CO2  and  found  to  be 

b  =  0.0003898, 
A  =  0.8249. 

Applying  the  correction  term  to  the  various  drops,  36  in  number, 
values  of  e213  were  obtained,  no  one  of  which  varies  from  61.085  X  io~8 
by  as  much  as  0.5  of  one  per  cent. 


366  LEO   JOSEPH   LASSALLE. 

III.  The  relationship  between  ei2/3  and  I/pa  was  found  for  values  up 
to  I  / pa  =  26,500.  The  value  of  A  =  0.8249  holds  until  I/a  =  0.50, 
approximately.  The  slope  of  the  curve  then  increases. 

The  values  of  I/a  for  CO%,  at  which  the  change  in  slope  begins  is  the 
same  as  that  found  by  Millikan  in  the  case  of  air. 

It  gives  me  pleasure  to  acknowledge  the  cheerful  and  able  assistance 
of  Dr.  Y.  Ishida  and  Mr.  B.  L.  Steele.  I  am  especially  indebted  to 
Dr.  R.  A.  Millikan,  who  suggested  the  problem  and  who  advised  me 
throughout  the  course  of  the  investigation. 

RYERSON  PHYSICAL  LABORATORY, 

UNIVERSITY  OF  CHICAGO, 

August  10,  1917. 


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